Is there any difference between "triangulate faces (Ctrl + T)" and "triangulate modifier"?
Traingulate modifier is non-destructive (it's a modifier) and you can choose which faces to triangulate based on their number of edges (i.e in some case you only want to triangulate ngons but not quads, like after a boolean operation that leave you with a messy mesh a part of your object and you don't want to spend time fixing it)